Cutting is frequently used in processes of manufacturing industrial products. For example, cutting is used for direct machining of products and machining of dies. When such cutting is performed, chatter vibrations may be generated on a tool. Chatter vibrations cause a deterioration in the shape of a finished surface or breakage of the tool.
Chatter vibrations include two types of vibrations; i.e., forced vibration and self-excited vibration. Forced vibration is a vibration which is generated when some forced causal vibration is amplified by the vibration characteristic of a machine. For example, intermittent cutting force generated during end milling or the like causes forced vibration. However, in some cases, the term “chatter vibration” does not encompass forced vibration. Self-excited vibration is a vibration which is generated when a vibration generated in a cutting process grows (i.e., is amplified) because of a presence of a closed loop that feeds back the generated vibration.
Major types of self-excited vibration include a regenerative type self-excited vibration and a mode-coupling type self-excited vibration. Regenerative self-excited vibration is generated, for example, when a vibration generated during cutting in a previous rotation or cutting by a preceding tooth has remained as an undulation of the machined surface, the uncut chip thickness fluctuates in time due to the remaining shape and a vibration at the present point. Mode-coupling self-excited vibration is generated, for example, when vibration modes in two directions have resonance frequencies close to each other and the vibrations in the two directions are coupled. Such chatter vibrations are collectively shown in the following Table 1.
[Table 1]
(a) forced vibration
(b) self-excited vibration
(b-1) regenerative self-excited vibration
(b-2) mode-coupling self-excited vibration
Therefore, techniques for suppressing chatter vibrations have been developed. For example, Patent Document 1 discloses an unequally divided end mill which has an odd number of cutting teeth and in which dividing angles different from one another are provided for the cutting teeth.